Pertubation theory for systems with strong short-ranged interactions

We propose a variant of thermodynamic perturbation theory based on the Mayer f-function which is applicable to strongly repulsive, and even singular interactions. The expansion of the free energy is successfully tested against known ‘exact results’ for hard-sphere fluids, and then applied to binary mixtures of particles with non-additive hard cores or shouldered potentials. The resulting phase diagrams agree well with existing simulation data and theoretical predictions.     

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids are calculated. Numerical results are given for equation of state and excess-free energy of the binary mixture of both additive and non-additive hard ellipsoids. It is found that the equation of state and free energy of mixtures increase with increase of anisotropy parameterx ₀.     

Perturbation theory for equilibrium properties of a binary mixture of hard discs

The radial distribution function (RDF) and thermodynamic properties of a two-dimensional hard-disc mixture are calculated by using the perturbation theory. Numerical results are given for theRDF, pressure and excess-free energy of the binary mixture of both additive and non-additive hard discs. It is found that the thermodynamic properties of the binary mixture of non-additive hard discs increase with Δ, the non-additive parameter.     

Weakly coupled mixtures of charged particles at zero temperature

The ground state energy, the excitation spectra and the structure factors of weakly coupled mixtures of charged particles (bosons or fermions) are obtained in the well-known framework of the Feynman diagrams. The general theory, which is developed in a first part, is then applied to the three kinds of binary mixtures obtained by combining fermions and bosons.     

Thermodynamics of III–V solutions with n components

A method has been developed for the calculation of phase diagrams of III–V mixtures with more than three components. The equations for the chemical potentials, activity coefficients and the free energy of the mixture and for the liquidus- and iso-solidus-concentration lines are given. The parameters, needed for the calculation, are the temperature of fusion, heats of fusion, and the interaction parameters. The interaction parameters can be fitted to datas of the binary or quasi-binary phase diagrams, or can be calculated using the electronegativities, energies of sublimation and molar volumes of the constituent elements.Two approaches for a mixture with n components are given, which give in the ternary and binary case the known equations. The two possible cases of quaternary III–V solutions are discussed explicitly.     

Excess thermodynamic properties of mixtures of Lennard-Jones liquids

The results of Monte Carlo calculations in the isothermal-isobaric ensemble are reported for a series of binary mixtures of Lennard-Jones liquids at zero pressure and a temperature of 115·8 K. In the case of equimolar mixtures comparison is made with the predictions of several recently developed theories of liquid mixtures. Particularly good results for excess Gibbs free energy and enthalpy are obtained from the variational theory of Mansoori and Leland and for excess volume from the one-fluid version of the so-called van der Waals model.     

Microstructure and thermodynamics of inhomogeneous polymer blends and solutions

A free energy density functional theory (DFT) for nonuniform polymeric mixtures is proposed based on first order thermodynamic perturbation theory. The segment-density based free energy functional provides an accuracy comparable to the numerically intensive polymeric DFTs while preserving the computational simplicity of an atomic DFT. The presented applications for solutions and blends of branched and linear polymers demonstrate the capability of the theory to capture the entropic and enthalpic effects governing the microstructure.     

The phase diagrams of a spin-1 transverse Ising model

The phase diagrams of the spin-1 transverse Ising model with the presence of a crystal field is investigated by using an effective-field theory (EFT). We give a method to calculate the Gibbs free energy numerically at finite temperature within the EFT. The first-order transition lines are obtained by comparing the Gibbs free energy. The phase diagrams and the Gibbs free energy are also compared with those given using the mean-field theory (MFT).     

On the critical non-additivity driving segregation of asymmetric binary hard sphere fluids

A previously proposed version of thermodynamic perturbation theory, appropriate for singular pair interactions between particles, is applied to binary mixtures of hard spheres with non-additive diameters. The critical non-additivity Δ_C required to drive fluid–fluid phase separation is determined as a function of the ratio ξ ≤ 1 of the diameters of the two species. Δ_C(ξ) is found to decrease with ξ and to go through a minimum for ξ ? 0.015 before increasing sharply as ξ → 0, irrespective of the total packing-fraction η of the mixture. These results are the basis of an estimate of the range of size ratios for which a binary mixture of additive hard spheres exhibit a fluid–fluid miscibility gap. This range is conjectured to be 0.01 ? ξ ? 0.1.     

Fourth virial coefficients for globular molecules

A binary mixture of hard rods with non-additive distances of contact, in one dimension, is studied. Special attention is paid to the case that two particles (hard rods) of the same species can come into contact in the presence of a particle of the other species between them. The system is treated by means of the ensemble which is specified by the total number of particles of one species, the chemical potential of the particles of the other species, the temperature and the pressure. The free energy in this ensemble is shown to be expressed by the eigenvalue with the smallest absolute value of an integral equation. The equation of state is obtained by numerical differentiation of the free energy.     

Nematic phase transitions in mixtures of thin and thick colloidal rods

We report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible fd virus) and thick (fd-PEG, fd virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, we observe a nematic-nematic coexistence region bound by a lower critical point. Moreover, we show that a rescaled Onsager-type theory for binary hard-rod mixtures qualitatively describes the observed phase behavior.     

Studies of a primitive model of mixtures of nonpolar molecules with water

The paper presents calculations of the properties of binary mixtures of hard spheres and directionally associating hard spheres, a simple model for mixtures of nonpolar molecules with water that was developed by Nezbeda and his coworkers. Extensive results from Monte Carlo simulations in the isobaric, isothermal ensemble are presented for the density, configurational energy and chemical potentials in the mixtures for fluid states over a range of temperatures, pressures and compositions. A species exchange technique is used to compute the chemical potential difference between components in the mixtures. The results obtained are compared with the predictions of first-order thermodynamic perturbation theory (TPT). It is found that this theory provides an accurate picture of the system over most of the conditions considered. Calculations are also made of vapour–liquid coexistence for the model using TPT and calculations of solid–fluid coexistence for the model using TPT and existing results for the free energy of the pure component solids. It is found that the vapour–liquid coexistence for the model is pre-empted by the solid–fluid coexistence, as had previously been found for the pure component directionally associating hard sphere system.     

二维二元替换式系统的统计理论

本文利用Collins模型研究二维二元替换式晶格系统。计算了系统的自由能,导出了溶解度和温度关系的曲线方程,并利用相平衡条件获得了和三维二元合金相类似的相图。 关键词：     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

Symmetry breaking patterns in superfluid He

By means of the time reversal operator a general form of the Landau free energy functional of superfluid ³He is investigated. Various possible phase diagrams of superfluid ³He in a magnetic field are discussed in the context of group theory. Both the cases of neglible and strong spin-orbit coupling are treated.     

Theory of vacancy formation energies in metallic alloys and in mixtures

A pair potential theory is developed for the vacancy formation energy in binary systems, in relation to liquid structure near melting. The theory makes the assumption that atomic relaxation round vacancies can be neglected: it is therefore appropriate to hot close-packed systems.While the theory is general, embracing metallic alloys and insulating mixtures like Ar-Kr, we have approximately evaluated the formula using the mean spherical approximation outside the cores, together with the Percus-Yevick theory for mixtures of hard spheres. These latter approximations are valid for Ar-Kr mixtures, but not for metallic alloys.     

Thermodynamic approach to phase coexistence in ternary phospholipid-cholesterol mixtures

We introduce a simple and predictive model for determining the phase stability of ternary phospholipid-cholesterol mixtures. Assuming that competition between the liquid and gel order of the phospholipids is the main driving force behind lipid segregation, we derive a Gibbs free energy of mixing, based on the thermodynamic properties of the lipids main transition. A numerical approach was devised that enables the fast and efficient determination of the ternary diagrams associated with our Gibbs free energy. The computed phase coexistence diagram of DOPC/DPPC/cholesterol reproduces well-known features for this system at 10 °C, as well as its evolution with temperature.     

Thermodynamics of pseudo-hard body mixtures

Thermodynamic properties of binary mixtures of hard spheres of various size and pseudo-hard bodies, mimicking the short-range non-additive repulsive interactions in realistic models of water, have been determined over the entire concentration range using standard NVT Monte Carlo simulations. Virial coefficients of the mixture have also been computed. Having no other theoretical tool currently available, a perturbed virial expansion is examined with respect to its potential to estimate/predict the properties of the mixture without resorting to any fitting of simulation data. The perturbed virial expansion is found to perform quite accurately for the mixtures containing larger spheres, whereas for small spheres dissolved in water the result is only qualitatively correct.     

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture.

Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N₂ and Ar and CH₄ are compared with experiment; the agreement is reasonable.